indirect utility function について

. It reflects both the consumer's preferences and market conditions.
This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility

v(p, w)

can be computed from his or her utility function

u(x),

defined over vectors

x

of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector

x(p, w)

by solving the utility maximization problem, and second, computing the utility

u(x(p, w))

the consumer derives from that bundle. The resulting indirect utility function is
:

v(p,w)=u(x(p,w)).

The indirect utility function is:
*Continuous on Rⁿ₊₊+ R₊;
*Decreasing in prices;
*Strictly increasing in income;
*Homogenous with degree zero in prices and income; if prices and income are all multiplied by a given constant the same bundle of consumption represents a maximum, so optimal utility does not change.
* quasi convex in (''p'',''w'');
Moreover, Roy's identity states that if ''v''(''p'',''w'') is differentiable at

(p^0, w^0)

and

\frac \neq 0

, then
:

-\frac=x_i (p^0,w^0),i=1, \dots, n.

== See also ==

* Expenditure function
* Hicksian demand function
* Gorman polar form

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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